T 291

TESTS OF HOLLOW TILE AND CONCRETE SLABSREINFORCED IN ONE DIRECTION

By Douglas E. Parsons and Ambrose H. Stang

ABSTRACT

Beams which represented sections of typical combination hollow tile andconcrete floor slabs reinforced in one direction were made and tested in thelaboratory for the purpose of obtaining information on the value of hollow

tiles in resisting bending and shearing stresses. The test pieces consisted of42 beams from 8 feet 10 inches to 15 feet 3 inches long, all 8 inches in depthand having a maximum width of 30 inches. For the purpose of comparison twoconcrete beams having the same sectional area as the gross sectional area ofthe composite beams and three concrete beams having the same sectional areaas the concrete ribs in the composite beams were also tested.

Observations were made of the deformation in the concrete, tiles and re-inforcement, deflection of the center of the beam, and development of cracks as

the loads were applied.Tables and curves give a summary of the test data, and comparisons are

made between these and the usual design computations for reinforced con-crete beams.

The results indicate that the tiles assisted the concrete in resisting bothbending and shearing stresses. The assistance of the tiles in resisting bendingstresses seemed to be approximately proportional to the modulus of elasticity

of the tiles. The assistance of the tiles in resisting shearing stresses varied

somewhat with the kind of tile, but, in general, added about 50 per cent to the

shearing strength of each concrete rib.

CONTENTSPage

I. Introduction 466

1. Purpose 466

2. Acknowledgments 467

II. Description of test beams 467

1. Design 467

2. Construction 46S

3. Storage 471

III. Auxiliary tests of the materials : 471

1. Reinforcement 471

2. Concrete 472

3. Hollow tiles 476

IV. Method of testing beams 477

465

466 Technologic Papers of the Bureau of Standards [vol. 19

Page

V. Results of tests and discussion 4791. General behavior of beams during tests 4792. Flexural tests on long beams 481

(a) Experimental data, methods of computation and no-

tation 481

(6) Concrete beams _

—

496

(c) Combination beams with no topping 4971. Concrete deformations, depth to the neutral

axis, deflections, and steel stresses 4972. Maximum bending moments and computed

stresses 500

3. Effect of mortar joints 504

(d) Combination beams with topping 504(e) Distribution of compressive deformations across

the beams 5063. Shear tests 506

(a) Beams without web reinforcement 506(b) Beams with web reinforcement 511

VI. General comments 512VII. Summary 514

I. INTRODUCTION

1. PURPOSE

In the design of floor slabs of a combination of hollow tiles andconcrete, reinforced in one direction, there has been an uncertaintyregarding- the extent to which the tiles could be relied upon to resistbending and shearing stresses. Slabs of hollow tiles and concretereinforced in two directions have been the subject of investigations

*

which have helped to establish a basis for their design. The actionof the tiles in these two types of slabs does not seem to be strictlyanalogous, for in the two-way type each tile is completely surroundedby the concrete, which seems to insure the transmission of stressesthrough the tile. In the one-way type, however, since the taking of

stress by the tiles depends almost entirely upon the adhesion existingbetween the tiles and the concrete, an analytical treatment must bebased upon so many assumptions and approximations that the re-sults could not be considered reliable unless confirmed by tests. Fewtests of this kind had been made. The Bureau of Standards, in

1 Slater, Hagener, and Anthes, Test of a Hollow Tile and Concrete Floor Slab Rein-forced in Two Directions, B. S. Tech. Paper No. 220. Larson and Petrenko, LoadingTest of a Hollow Tile and Reinforced Concrete Floor of Arlington Building, Washington,D. C, B. S. Tech. Paper No. 236.

Parsonsj

Tests of Hollow Tile and Concrete Slabs 467

cooperation with the Hollow Building Tile Association, therefore,conducted a series of tests in order to obtain information which

might serve as a basis for design. The tests were planned to obtaininformation on (1) the value of the tiles in resisting bending and

shearing stresses, (2) the effect of the physical properties of the tiles,

(3) the effect of mortar in the cross joints between the tiles.

2. ACKNOWLEDGMENTS

The Hollow Building Tile Association, Chicago, 111., cooperatedby Pavmg f°r the construction of the test beams. Their representa-tive, F. J. Huse, chief engineer of the association, assisted in plan-

ning the investigation. The bureau staff supervised the constructionof the beams, made the tests, and prepared this report.The authors are indebted to several members of the bureau staff,

especially to S. H. Ingberg, W. A. Slater, and N. D. Mitchell fortheir advice and assistance.

II. DESCRIPTION OF THE TEST BEAMS

i. DESIGN

The tests were made on beams representing sections of typicalfloor slabs. The size of the beams was chosen so that they could beconveniently loaded in a testing machine. The dimensions and de-tails of the beams are shown in Figures 1 and 2. All beams had atotal depth of about 8 inches. Those beams containing tiles con-sisted of two 4-inch concrete ribs separated by a single row of tiles,laid with their cells parallel to the length of the beam, and inclosedon each side by a row of tile sections which had been cut to includebut one vertical shell and one vertical web. The cutting of the tilesso as to include less than one-half their total width was necessary onaccount of the limits imposed by the clearance between the screws ofthe testing machine. The beams were assumed, however, to be equiv-alent to two units of width in a completed floor slab where eachunit of width is a strip 16 inches wide consisting of one 4-inch rein-

forced concrete rib and one-half of each of the adjacent rows of tiles.The joints were staggered to bring the joints of the outer tiles

opposite the centers of the middle tiles. The solid concrete beamsA and / (figs. 1 and 2) had the same sectional area as the gross sec-tional area of the composite beams, and the concrete beams B (fig. 1)had the same sectional area as the area of the concrete ribs in thecomposite beams.

468 Technologic Papers of the Bureau of Standards ivoi. m

The long beams were made to represent freely supported slabs andthe short beams were made to represent sections of slabs continuousover supporting girders. General views of these are given in Fig-

ures 3 and 4.

The beams had more reinforcement than is commonly used infloors. Previous tests 2 have indicated that test beams constructed

with the usual percentage of reinforcement ordinarily fail by yield-

ins: of the steel in tension. Since in these tests it was desired to

study the comparative value of the concrete and hollow tiles in re-

sisting stresses, a higher percentage of reinforcement was used.

Four %-inch round deformed bars were used as tension reinforce-

ment in each beam. Based on the sectional area of the concrete

only, this gives 1.27 per cent reinforcement for the 29-inch solid

concrete beams (A, fig. 1 and /, fig. 2) and the long combination

beams with topping (H, fig. 1) and 4.58 per cent for all the other

beams. The bars in the long beams (bars A, fig. 1) were anchoredwith semicircular hooks beyond the supports, and the combination

beams were provided with a concrete section at each end to join the

two units. On the short beams the distance which the bars (barsD, fig. 2) were embedded in the concrete was depended upon to

prevent slipping.

2. CONSTRUCTION

The beams were made by a local contractor experienced in thistype of building construction. He was instructed to make the testpieces with the same care that is ordinarily used for construction

of this kind. The labor and all of the materials except the tileswere supplied by the contractor. Since the contract was awardedon a lump-sum basis, there was no incentive for the contractor toproduce specimens superior to those desired.

In order that the beams might be approximately the same agewhen tested, the construction was extended over a period of nineweeks. All of the beams constructed in one week were made on thesame day. The first 14 beams made were constructed outdoors, butfor convenience in moving, the remaining beams were constructed ina laboratory having an overhead crane. The date on which eachbeam was made is included in Table 6.

2 See, for instance, National Fire Profing Co., " Collation of tests of the resistingqualities of Natco hollow tile fireprooflng," 1914. Building Research Board of GreatBritain Special Report No. 2, " Experiments on floors," London, England, October, 1921.

Parsons "|Stanff A

Tests of Hottoiv Tile and Concrete Slabs 469

The wood forms for the beams were prepared and the reinforce-ment and tiles placed before any of the concrete was placed, so that

the concrete for all the beams to be made on that day could be poured

Beams A-l. A-2 ? ? 6cx)9 Lines

\Si H -0IS'- o'

-Bars A ~W\2 -0mmiI I ~VSV- -,-,.,-h

Beams B-l, B-2. B-3

rwH--0is'-a"

- Bars A "TDiT HTH

Beams C-l, C-2. C-3. D-I.D-2, 0-3, L-i.L-Z. E-3.,l j" : .,'. ^ J;

.

. ;,! . . ,„I I [:

Safe Lines

lv-iJ-U-UJ-LJJ-UJ-LUJ_LLlttliiJ-i-bl pffih

1+-0is'-o"

7Beams F-I.F-2.F-3, G-),G-Z, Q-3

3^g^g^S^3^3l^3 ; ,v

/£" Morfar joints-

icU-UJ-LJ-LtUJ-iJ-U-LLU-LLU-LiJ-LtlI (|)

, .N BarsA Cl) , 'l rtr-*'-&\ |

i*-ois -a"

9—9 Sara B - £-f /4perfBg

470 Technologic Papers of the Bureau of Standards [vol. ia

8 -laS'-Cx — » -< i

(l) BarsD—^ Bans Br\(J)

Beam I-lBars C

»'i

1 Z'S'—

I

fflj

r^y-j^-i J—i- ~j— ».- ——— '—I ~i-^X-^zj^x^lBarsC

Beams J-l, J-2, J-J, to**,

3^K-kK-Z.K-3,lzKL?Z.±3

Y—*s ——

I

*

SareC

Beams M-l, M-2, M-3 ^l -K|-«--|+T- |v

-rt

',; -ftf-'lr^^^b^

*1 -.- • *; "*•*:'.*.* >i ' J'«:/

;'. 1 i

'',"'•'

1 1 l-.^-.v-.',-' ... I 1 1

Cars C

Ssoms AW, N-2, N-3

S -10f'-t,'J- S-i : 1 HL

(I) Bow D^ yBan)B-(T)

Bore_C

6eo/r»3 0-/, 0-2, 0-3 !r^

-Li^a=a33

.— e'-s 1

BonsC

Technologic Papers of the Bureau of Standards, Vol. 19

Fig. 3.

—

Beams stored in the laboratory

Technologic Papers of the Bureau of Standards, Vol. 19

Fig. 4.

—

Side view of beams stored in the laboratory

Fig. -Hollow tiles

Lot 1: 3-cell, by 12 by 12 inch partition tile of Indiana surface clay.Lot 2: 6-cell, 8 by 12 by 12 inch load-bearing wall tile of Indiana surface clay.Lot 3: 6-cell, 8 by 12 by 12 inch load-bearing wall tile of Ohio Are clay.Lot 4: 6-cell, 8 by 12 by 12 inch load-bearing wall tile of Kentucky shalo.

Parsons i pests of Hollow Tile and Concrete Slabs 471o Fa H{/ j '

The aggregate was proportioned by loose volume with the wheel-

barrows used to transport the materials to the mixer. One bagof Portland cement weighing 94 pounds was assumed as 1 cubic

foot. This method of proportioning was not accurate, but as the

laborers were careful in properly filling the wheelbarrows, the

volumes of which had been previously determined, the average ofseveral batches probably approximated the desired proportions.

The mixing water was not prescribed but was determined by theworkman who placed the concrete in the forms. The workman haddifficulty in placing the concrete in the 4-inch ribs containing two%-inch reinforcing bars unless the concrete contained sufficient water

to flow quite readily. This difficulty was increased somewhat bythe absorption of part of the mixing water by the tiles. Conse-quently, the concrete as it came from the mixer was not of uniformconsistency, but always contained sufficient water to flow readily

from the wheelbarrows into the 4-inch spaces between the rows oftiles. Only a small amount of puddling with a shovel was done.

3. STORAGE

When there was danger of injury to the concrete from freezing,the beams which were stored outdoors were covered with canvasand straw; at other times they were exposed. The beams were notremoved from the forms until they had aged for at least threeweeks. They were then piled in the laboratory as shown in Figures3 and 4. The duration of the outdoor and indoor storage is in-cluded in Table 6. The temperature of the laboratory in which thebeams were stored varied between 65 to 75° F. Because the labora-

tory was heated the relative humidity was much less than of theair outside, and for this reason the beams and control specimens

of concrete, which were fabricated indoors, were sprinkled once each

day on the three days immediately following their construction.

III. AUXILIARY TESTS OF THE MATERIALSi. REINFORCEMENT

The tension reinforcement in all beams consisted of round de-formed billet steel bars, % inch in diameter. Round deformed bars% inch in diameter were used for transverse reinforcement in thebeams having a concrete topping. The reinforcement was supplied

by the contractor, who purchased it in the open market. Fivecoupon specimens were tested for modulus of elasticity, propor-

tional limit, yield point, tensile strength, and elongation. The re-sults of the tests are given in Table 1. It is seen that this material

43356°—25 2

472 Technologic Papers of the Bureau of Standards ivoi. 19

corresponds to the structural-steel grade for deformed billet steel

concrete reinforcement bars as specified by the American Society

for Testing Materials in their specifications A 15-14. 3

Table 1.

—

Tensile tests of reinforcement

[%-inch round deformed bars]

NumberPropor-tionallimit

Yieldpoint

Tensilestrength

Modulus ofelasticity

Elongationin 8 inches

1 _ _

Lbs./in. 2

38, 50039,00038, 60024, 20039,600

Lbs./in. 2

39,70039, 30039,40037,50040,000

Lbs./in. 2

54,50056,90059,00057,20058,800

Lbs./in. 2

29, 400, 00028, 900, 00029, 000, 00028, 600, 00029, 000, 000

Per cent32.0

2 ___ _ 30.03

427.529.0

5 30.0

Average 35, 980 39, 180 57,280 28, 980, 000 29.7

2. CONCRETE

The materials used in making the concrete were all purchased bythe contractor on the local market. The concrete consisted of 1part Portland cement, 2 parts Potomac River sand, and 4 parts%-inch Potomac River gravel and was mixed in a drum mixer. Theconcrete in the seven beams first constructed was not tested, but foreach of the others two control specimens were made. These wereboth compressive specimens—one a 6 by 12 inch cylinder cast in astandard 4 steel mold and the other an 8 by 8 by 12 inch-right prism.Two of the 8 by 12 inch sides of the forms for these prisms werecomposed of the same kind of material, either tile or wood, that wasin contact with the concrete in the corresponding beam, and theother two sides and the bottom of the forms were made of oiledwood. All control specimens were stored with the beams within 48hours from the time they were cast.The concrete cylinders and prisms were tested at approximately

the same age as the corresponding beams. Their compressivestrength and modulus of elasticity were determined. Deformationsin the concrete were measured over an 8-inch gauge length with aclamp type of compressometer having a single micrometer dial read-ing to 0.0001 inch. The results of these tests are given in Table 2.

3 American Society for Testing Materials Standards, 1924, p. 141.*" Standard method of making and storing specimens of concrete in the field, C 31-21,"

American Society for Testing Materials Standards, 1924, p. 762.

Parsons i Tests of Hollow Tile and Concrete SlabsStang J ' 473

Table 2.

—

Compressive tests of concrete

[Age at test from 102 to 106 days. Storage the same as for corresponding beams]

Date poured

6 by 12 inch cylinders 8 by 8 by 12 inch prisms

Number Com-pressivestrength

Modulusof elas-ticity

Com-pressivestrength

Modulusof elas-ticity

Form material

E-2 Dee. 7, 1923do

Lbs.I'm. 2

2,2301,9501,5301,0602,050

Lbs./in.

'

2, 180, 0001, 910, 0001, 770, 0001, 720, 0002, 020, 000

Lbs./in. 1

2,7302,1202,4502,5303,310

Lbs./in.'

Shale tiles.D-2D-3 do Do.G-2 do

doDo.

H-3 Surface-clay tiles.

1,760

Dee. 14,1923do

E-3 - 990850

1,100880

1,130

1, 860, 0001, 450, 0001, 780, 0001, 540, 0002, 160, 000

1,5601,4501,4901,8001,570

2, 540, 0001, 650, 0001, 210, 0002, 220, 0002, 150, 000

Shale tiles.A-2 Wood.B-3 do Do.N-l do Fire-clay tiles.K-l do Do.

990

Dec. 21,1923dodo

N-2 _._ - 1,260850

• 1, 2201,3101,250

1, 780, 000970, 000

2, 140, 0002, 440, 0001, 700, 000

2,2101,8502,6402,1401,700

2, 450, 0001, 900, 0003, 300, 0002, 190, 0001, 710, 000

Do.M-l0-1

Do.Surface-clay tiles.

L-l. do Shale tiles.Extra do Wood.

1,180

Dec. 28,1923do

0-1... - 1,1401,0301,0101,3801,360

1, 700, 0001, 670, 0001, 650, 0002, 320, 0001, 740, 000

3,0802,3702,3301,7901,960

3, 390, 0002, 460, COO3, 060, COO3, 420, 0002, 500, 000

Surface-clay tiles.C-2. ... Do.F-lG-3--

dodo

Do.Fire-clay tiles.

L-2 do Shale tiles.

1,180

Jan. 4, 1924do

C-3 1,110990880820

1,030

1, 670, 0001, 380, 0001, 430, 0001, 370, 0001, 410, 000

1,2401,7801,3301,4301,240

2, 040, 0002, 550, COO2, 080, 0002, 560, 0002, 020, 000

F-2 Do.J-l do Do.K>2.. • doM-2--- do Do.

970-

Jan. 11,1924do

F-3 450530720560470660

990, 000900, 000

1, 240, 0001, 050, 000970,000

1, 050, 000

1,4401,1501,2401,0301,3301,020

2, 040, 0002, 020, 0002, 080, 0001, 940, 0001, 960, 000

J-2 Do.0-2... do Do.K-3 doM-3.__ do Do.1-1 do Wood.

Average 570

Jan. 18,1924do

N-3 _ 1,470950

1,0701,1401,170

1, 740, COO1, 750, 0001, 480, 0002, 000, 0001, 960, 000

1,5701,5001,6501,7301,430

1, 670, 0002, 180, 0002, 020, 0002, 600, 0001, 060, 000

Fire-clay tiles.Surface-clay tiles.

Do.J-30-3. do..L-3 doExtra do Wood.

Average 1,160

474 Technologic Papers of the Bmreau of Standards ivoi. io

It is believed that the average strength of the concrete in the

beams was greater than the strength of that in the cylinders, sincesome of the most important, factors affecting the strength of con-crete were different for the cylinders and the beams. The steelmolds for the cylinders were substantially water-tight and there-fore confined the excess mixing water while the concrete was set-ting. After the molds were removed the excess moisture evapo-rated, leaving voids or pores. The forms for the concrete in thebeams were porous, and this, together with the cracks between theboards of the wooden forms and between the tiles, permitted muchof the excess water to escape before the concrete had set. Experi-ments have shown that the removal of some of the excess mixingwater before the initial set has taken place increases the strength

of the concrete by reducing its volume, its water-cement ratio, andits porosity.5 Furthermore, many other experiments have shownthat the presence of moisture during the curing of concrete is es-sential for the proper hydration of the cement, and that concretewill gain but little strength after the first three weeks when curedin dry air.6 The curing conditions for the cylinders were thereforevery unfavorable for the development of normal strength, since the

relatively small volume of concrete in proportion to the large sur-face area exposed to the dry air of the laboratory permitted a rapid

drying of the concrete, which prevented the normal hydration of the

cement. The moisture which had been absorbed by the forms andtiles surrounding the concrete in the beams probably had the effectof retarding the loss of moisture, and this, together with the smaller

ratio of the exposed surface area to volume, created a more favor-

able curing condition for the concrete in the beams than for the con-

trol cylinders.

The strength of the concrete in the prisms was probably morenearly equal to the strength of the concrete in the beams than that

in the cylinders. The forms for the prisms, like those for the beams,were not water-tight and, the materials of which the forms were

made being the same as those which surrounded the concrete in thecorresponding beams, had about the same porosity. Furthermore,

5 Abrams, " Effect of vibration, jigging, and pressure on fresh concrete," Proc. Amer.Concrete Inst., 15, 1919. Wig, Williams, and Gates, Strength, and Other Properties ofConcretes as Affected by Materials and Methods of Preparation. B. S. Tech. Paper,No. 58.

'

6 Wig, Williams, and Gates, Strength and Other Properties of Concretes as Affected byMaterials and Methods of Preparation. B. S. Tech. Paper No. 58. Abrams, Effect ofCuring Condition on the Wear and Strength of Concrete, Bui. 2, Structural MaterialsResearch Lab., Lewis Inst., Chicago. Abrams, Flexural Strength of Plain Concrete, Bui.11, Structural Materials Research Lab., Lewis Inst., Chicago. Green, " Relation betweenmethods of curing standard concrete test specimens and their comparative strength at28 days," Proc. A. S. T. M., 19, Pt. II. Gonnerman, " Effect of age and condition ofstorage on the strength of concrete," Proc. Amer. Concrete Inst., 14, 1918.

B%%T] Tests °f H°tt°w Tile a7ul/ Concrete Slabs 475

the ratio of the area of concrete directly exposed to the air to the

volume of concrete in the prisms, though greater than the ratio for

the beams, was less than that for the cylinders. The effect of theabsorption of some of the excess mixing water by the form material

upon the strength of the concrete is dependent upon the rate atwhich the water is absorbed.

Some published 7 and unpublished experiments made at the Bureauof Standards have shown that most of the water absorbed by burned-clay bodies similar in size and composition to hollow tiles will beabsorbed in the first few minutes after immersion. Usually 60 to 70per cent of the ultimate absorption will be taken up in 5 minutes and70 to 80 per cent in 15 minutes. Although the conditions which exist

in a form are quite different, it is evident that the tiles did absorbwater rapidly. It is probable that most of the water absorbed bythe tiles was taken up very soon after the concrete was placed, andtherefore this absorption increased the strength of the concrete.

The difference in the shapes of the test specimens tended to causea further difference in the strength of the prisms and cylinders. Theratio of length to least dimension for the cylinders was 2 and for theprisms 1.5. Some tests 8 indicate that this would cause the prisms toresist stresses approximately 5 per cent greater than would the cylin-

ders if the quality of the concrete were uniform.

The strength of the concrete, as indicated by the tests on the con-trol specimens, differed greatly from week to week. Large differ-ences in the strength of concrete which is made without a carefulproportiong of the aggregate and amount of mixing water are notunusual. One cause was the lack of uniformity of the aggregatefrom week to week. Nearly all of the aggregate used on one day wastaken from one delivery and for this reason was probably quite uni-form. Although no tests were made of the aggregate, it was notice-able that the material used on January 11 was finer than that usedon other days and that it contained a large amount of silty ma-terial. Another cause was the amount of mixing water used whichnot only differed from batch to batch but probably also from weekto week.

No definite conclusions can be drawn concerning the averagestrength of the concrete in the beams. For the purpose of design it

is commonly assumed that a 1:2:4 mix will produce a concretehaving an ultimate strength of 2,000 lbs./in. 2 when tested in theform of standard cylinders 28 days old, made, and stored underlaboratory conditions, but it is known from numerous tests of field-

7 Foster, " Effectiveness of different methods of making absorption determinations,"Jour, of the Amer. Ceramic Soc, 6, No. 5, 1923.

.8 Report of Committee on Specifications and Methods of Tests for Concrete Materials.

Proc. Amer. Concrete Inst., 10, 1914.

476 Technologi-c Papers of the Bureau of Standards [voi.19

made 1:2:4 concrete that the strength is frequently, if not usually,much less than 2,000 lbs./in. 2 9

Taking into consideration the age of the test pieces and the

storage conditions, it seems probable that the average strength of

the concrete in the beams was within the range usually obtained inbuilding construction.

3. HOLLOW TILES

Four different lots of tiles were used : ( 1 ) 3-cell 6 by 12 by 12inch partition tiles made of Indiana surface clay, (2) 6-cell 8 by 12by 12 inch load-bearing wall tiles made of Indiana surface clay,

(3) 6-cell 8 by 12 by 12 inch load-bearing wall tiles made of Ohiofire clay, (4) 6-cell 8 by 12 by 12 inch load-bearing wall tiles made ofKentucky shale. The types of tiles are shown in Figure 5.Ten tiles from each lot were selected by appearance and their

physical properties determined. Each tile was loaded parallel tothe direction of the cells and the modulus of elasticity and compres-

sive strength determined. The deformations were measured overan 8-inch gauge length with a clamp type compressometer having a

single micrometer dial reading to 0.0001 inch. The absorption wasmeasured on three pieces containing from 12 to 20 square inches offace area taken from each tile after the compression test. These

were first dried to constant weight, immersed in cold water, raised to

the boiling point in one hour, and boiled for four hours. Theywere then permitted to cool to room temperature and weighed.- The results of the tests of the tiles are given in Table 3. Thedeformations taken to within 70 per cent of the ultimate strength

of the tile were proportional to the loads applied. Table 3 shows

that the 3-cell 6 by 12 by 12 inch Indiana surface clay tiles would beclassed as " soft " according to the tentative specifications for hollow

burned-clay partition tile C 56-24T of the American Society forTesting Materials. The 6-cell 8 by 12 by 12 inch Indiana surfaceclay tiles would be classed as " soft " according to the tentative speci-

fications for hollow burned-clay load-bearing wall tile, C 34-24T, ofthe same society, and the 6-cell 8 by 12 by 12 inch Ohio fire-clay

tiles and the 6-cell 8 by 12 by 12 inch Kentucky shale tiles would

be classed as " hard " according to the sanie specification.

9 Thompson and Nichols, discussion, " Compressive strength of concrete in flexure,"Proc. Amer. Concrete Inst., 18, 1922.

parsons 1 Tests of Hollow Tile and Concrete SlabsStan-Cr -1 '

477

Table 3.

—

Compressive tests of the tiles

[Loads applied on open ends of tiles]

ThicknessWeight

Compressivestrength

Refer-encenum-

Totalweight

ofconstit-

uent

Ab-sorp-tion

Modulus

Hollow tiles Ver- Ver-of

elasticity

ber tical tical mate- Gross Net (net area)shell webb rial area area(s) (w)

Inch Inch Lbs. Lbsjin? Lbs.linS Lbs.lint Per cent Lbs./inJ( 1 0.80 0.76 21.7 0. 0590 1.200 2.760 24.7 1, 820, 000

2 .80 .70 21.2 .0581 890 2,080 26.0 1, 400. 0003 .80 .69 21.2 .0589 1.340 3.150 26.0 1, 640, 000

Lot No. 1, 3-cell 6 by 12 by12 inch Indiana surfaceclay.

4

56

.77

.81

.80

.68

.69

.69

22.020.821.3

.0628

.0581

.0590

1.4001.1601.350

3.2902.7003.140

21.926.226.1

2, 400, 0001, 470, 0001, 510. 000

7 .81 .69 21.0 .0573 1.200 2,780 27.9 1, 690, 0008 .81 .69 21.7 .0590 1,180 2,740 26.0 1, 460, 0009 .81 .69 21.0 .0587 1,200 2,800 25.6 1, 510, 00010 .81 .69 21.3 .0587 1,200 2,760 24.6 1, 960, 000

Average .80 .70 21.3 .0590 1,210 2,820 25.5 1,686,000

I 1 .89 .63 31.0 .0610 1,630 3,690 23.2 1, 950, 0002 .87 .63 30.5 . 0609 1,220 2,790 23.8 1,610,0003 .86 .62 30.3 .0609 1,310 2,980 24,2 2, 000, 000

Lot No. 2, 6-cell 8 by 12 by12 inch Indiana surfaceclay.

456

.88

.87

.86

.63

.63

.64

30.729.529.3

.0608

.0590

.0596

1,1401,0901,080

2,6102,5002,500

24.125.925.3

1, 570, 0001, 510, 0001, 165, 000

7 .89 .64 31.0 .0604 1,270 2,870 24.7 1, 490, 0008 .87 .63 31.2 .0613 1,200 2,700 23.4 1, 770, 0009 .87 .64 30.5 .0611 1,270 2,930 24.1 1, 450, 00010 .89 .62 31.2 .0626 1,100 2,500 22.7 1, 710, 000

Average .88 .63 30.5 .0608 1,230 2,810 24.1 1, 623, 000

f1 .78 .59 34.3 .0717 1,380 3,520 12.9 3, 160, 0002 .76 .61 34.7 .0748 1,720 4,500 12.6 3, 510, 0003 .77 .60 34.7 .0720 1,550 3,980 13.0 2, 180, 0004 .77 .60 34.5 .0722 1,710 4,350 12.4 2, 600, 000

Lot No. 3, 6-cell 8 by 12 5 .75 .59 34.0 .0759 2,820 7,270 8.6 4, 540, 000by 12 inch Ohio fire clay. 6 .75 .59 34.3 .0739 1,950 5,020 11.2 4, 040, 000

7 .76 .61 34.5 .0753 2,380 6,210 9.7 4, 220, 0008 .77 .60 35.5 .0746 1,690 4,300 10.2 5, 250, 0009 .79 .59 34.7 .0721 2,210 5,580 12.4 3, 400, 00010 .77 .59 34.3 .0755 2,300 5,820 11.4 3, 440, 000

Average .77 .60 34.5 .0738 1,970 5,050 11.4 3, 634, 000

( 1 .82 .60 37.0 .0790 2,120 5,020 6.8 5, 340, 0002 .82 .62 36.2 .0760 3,310 5,370 8.1 4, 300, 0003 .84 .62 36.7 . 0756 1,540 3,560 9.8 3, 500, 0004 .79 .61 36.3 .0755 2,100 4,840 8.7 4, 250, 000

Lot No. 4, 6-cell 8 by 12 by 5 .81 .60 37.2 .0810 2,970 7,150 7.8 5, 060, 00012 inch Kentucky shale. 6 .82 .62 36.5 .0746 2,910 6,770 10.4 6, 850, 000

7 .80 .60 36.3 .0770 2,490 5,850 9.5 5, 900, 0008 .82 .58 37.5 .0808 2,850 6,740 7.5 5, 850, 0009 .82 .60 37.0 .0811 3,000 7,110 6.2 6, 000, 00010 .84 .61 36.3 .0724 1,280 3,000 14.6 3, 050, 000

Average .82 .61 36.7 .0773 2,460 5,540 8.9 5, 010, 000

IV. METHOD OF TESTING BEAMSBefore placing1 the beams in the testing machine they were

measured, marked for the positions of the loads and supports, andthe holes drilled in the concrete, tiles, and reinforcement, so thatstrain-gauge readings could be taken. The measurements includedthe total breadth of the beams, measured at intervals of 2 feet alongtheir length, and the depth from the top of the concrete to thecenters of the two outside reinforcing bars which had been exposedfor strain-gauge measurements. The locations of the 8-inch gauge

478 Technologic Papers of the Bweau of Standards ivoi.io

lines on which strain measurements in the concrete, tiles, and steel

were made are shown in Figure 1.The beams were tested in a vertical screw universal testing ma-

chine having a capacity of 600,000 pounds. The moving head ofthe machine applied its force through a spherical bearing to a load-

ing beam as shown in Figure 6. At the lines of the loads andsupports steel plates 8 inches wide and 1 inch thick and extending

the full breadth of the beams were embedded in plaster of Paris

in order to distribute the pressure uniformly. The long beams

A.4-'

Loads

L Z2O Reaction Reaction OT* 14-' A

A. BEND TEST FOR LONG BEAMS

j* 10'OR //' HLJj. Load lanri Ql

Reaction Reaction

Af' ?B.SHEAR TEST FOR LONG BEAMS

5'0R5k'h 5 OR5k —HLA Loads £L

YReactionC SHEAR TEST FOR SHORTBEAMS

Fig. 7.

—

Loading diagram for test beams

were supported with a span of 14 feet (fig. 7 A B). The shortbeams were supported on the concrete blocks which represented the

stems of supporting girders (fig. 7 C).

The testing of the long beams was divided into two stages. Theobject of the first test was to cause high bending stresses and ofthe second test to develop high shearing stresses. Accordingly, the

loads for the first test were spaced 2 feet each side of the centers

of the beams (fig. 1 A) and for the second test were placed fromiy2 to 2 feet from the nearest supports, as shown in Figure 7 B.Figure 6 shows the set-up for the shear test. The short beams were

Technologic Papers of the Bureau of Standards, Vol. 19

Fig. 6.

—

Beam E-l in the testing machine for shear test

Parsons -i Tests of Hollow Tile and Concrete Slabs 479

loaded continuously to failure, the loads being applied either at 2.5

or at 2.75 feet from the centers of the beams, as shown in Figure 7 G.

In loading the long beams, to produce high-bending stresses, it

was desired that the maximum loads applied be as near the maxi-mum, as determined by the ultimate strength of the construction inflexure, as could be without injuring the beams to such an extent

as to make them unfit for the shear tests. An 8-inch strain gaugewas clamped on each of the two outside reinforcing bars to measure

their deformations. A strain gauge was also used to measure thecompressive deformations in the concrete and tiles. The deflectionwas measured at the centers of the beams on mirror scales gradu-

ated to 0.1 inch, by means of a fine wire supported directly over the

supports and kept taut by rubber bands as shown in Figure 6. Be-fore a load was applied on a beam a set of zero observations wastaken on all gauge lines and the center deflection read. An incre-ment of load was then applied and a second series of observations

taken. The amount of each load increment was chosen so as tosecure at least five series of observations for each beam before fail-ure. During the test cracks were noted as they became visible. Theloading was continued until the strain-gauge readings indicatedthat either the steel had been stressed well beyond the yield pointor the deformation in the concrete was near the amount which maybe expected in a compression failure of a beam.

The loads were then applied nearer the supports for the sheartest. The position of the loads and span between the supports aregiven in Table 6 and shown in Figure 7.The deformations and deflection readings and the record of the

cracks were taken on the short beams in the same manner as onthe long beams. On account of the manner of loading there was nolength over which the bending moment was constant. The gaugelines were located as near to the centers of the beams as the locationof the concrete blocks and the necessary clearances for the apparatuswould permit, and their positions with respect to the centers of thebeams were recorded. These readings made it possible to distin-guish between failures due to the yielding of the tension reinforce-ment and those directly due to compression failure of the concreteand tiles.

V. RESULTS OF TESTS AND DISCUSSIONi. GENERAL BEHAVIOR OF BEAMS DURING TESTS

The behavior of the combination beams during the tests was simi-lar to that of the concrete beams. The shapes of the load-deforma-tion curves and the load-deflection curves shown in Figures 8 9 10

43356°—25 3

480 Technologic Papers of the Bioreau of Standards [roi.19

and 11 do not differ materially from those which have been obtainedfrom tests made on concrete beams having about the same ratio ofreinforcement. The chief difference noted was that the maximumaverage compressive deformation over an 8-inch gauge length in the

concrete of the combination beams without topping immediately pre-

ceding a compression failure was less than in the concrete beams.The load-deformation curves for the tiles were similar in shape tocorresponding curves for the adjacent concrete.

Tension cracks across the bottom of the beams were visible in thetiles at the same time that they could be seen in the concrete. These

cracks formed an irregular but continuous line across the beam with-out changes in the directions of the cracks where the concrete andtiles joined. No tendency for the cracks to follow the joints betweenthe tiles-could be observed.

Diagonal cracks which appeared in the outside tiles of some of

the beams were found, after breaking the beam, to* be in approxi-

mately the same plane and to have about the same length as oppo-

site cracks in the concrete. The joints between the tiles did notappear to change the direction or affect the development of diagonal

cracks.

The bond between the concrete and tiles was sufficient to resistthe tendency of the tiles to break away from the concrete until afterfailure of the beams had occurred from some other cause.

Since the loads were applied by a testing machine, it was possible

to watch the progress of the compression failures by observing thedeformation and spalling of the concrete and tiles. In the beams

which failed in compression the failure of the concrete and tiles

seemed to occur simultaneously.

In the beams with open joints between the tiles there must have

been a concentration of stress in a portion of the concrete opposite

the joints. Even though the staggered joints aided in relieving this,the stress in a small volume of concrete adjacent to a joint was prob-ably much greater than the average stress in the concrete within thegauge length. It may even have been higher than would havecaused failure in a solid concrete beam, since these highly stressed

portions were surrounded and supported by a relatively large volumecarrying lower stresses. Evidence of similar action is found inrecords of tests of beams and compression members. Beams whichfail in compression do not fail until the strain in the concrete isgreater than would cause the failure of a compression test specimenof usual dimensions. Tests show that when a load is applied to arelatively small portion of a concrete surface higher stresses will beresisted than when the entire surface is loaded.10 It seems probable

10 Taylor and Thompson, " Concrete plain and reinforced," 1916, p. 330.

Parsons "1Stany J

Tests of Hollow Tile and Concrete Slabs 481

that very high stresses could and probably did occur in small vol-umes of the concrete opposite joints without causing failure of thecombination beams. It is, however, probably due to these concen-

trated stresses that the average compressive strains observed in the

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482 Technologic Papers of the Bureau of Standards [vol. 19

deformations in the concrete and reinforcement for beams C, D, E,

F, and G were determined from the strain-gauge readings taken onbut one gauge line on each material, and the deformations shownfor beams A, B, and H are the average of measurements taken ontwo gauge lines of each material. The deformations given are

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Fig. 9.

—

Load-deformation curves for concrete and steel, load-deflection curves,

and values of ko for the long beams C and DThe elongations in tbe reinforcement are shown by circles and the compressions in the

concrete by crosses.

those measured in the concrete at the extreme fiber and in the steel

at the bottom of the bars. Each point on the load-deflection curvesis the average of the two measurements taken, one on each side of

the beam. In the same figures are given the experimentally deter-

mined depth of the neutral axis expressed as a fraction Jc of the dis-

ParsonsStang

Tests of Hollow Tile and Concrete Slabs 483

tance d from the compression surface of the beam to the center of thereinforcement. These were calculated from the deformations on the

assumption of a linear distribution of strain over the cross section.

Tables 4 and 5 summarize the data of the bend tests on the long

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Load-deformation curves for concrete and steel, load-deflection curves,and values of fco for the long beams E and F

The elongations in the reinforcement are shown by circles and the compressions in theconcrete by crosses.

beams. In Table 4 are given the construction data for the beamsand a comparison of observed stresses and strains at loads belowthe maximum, with corresponding values computed from certainempirical assumptions. The values given correspond to three dif-ferent loads, marked in the table as numbers 1, 2, and 3.

484 Technologic Papers of the Bureau of Standards ivoi. 19

1. It was desired to study the behavior of the beams under con-ditions corresponding as nearly as possible to the conditions underthe usual design loads. For this reason load number 1 was chosenfrom the test loads by selecting the load which gave (a) an averagetensile strain in the steel greater than 0.00017 inch per inch. This

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]Tests °f Hollow Tile and Concrete Slabs 485

per inch, corresponding on the basis of a modulus of 29,000,000lbs./in. 2 , to the usual design stress of 16,000 lbs./in.2

3. Load number 3 was similarly interpolated to give a measureddeformation in the steel of 0.0011 inch per inch corresponding to

a stress of 32,000 lbs./in.2 , double the usual design stress.

All computations were based upon the usual assumptions for re-inforced concrete beams. These are as follows

:

1. A plane section before bending remains plane after bending.2. Adhesion between the concrete and steel is perfect.

3. In calculating the resisting moment the tensile resistance ofthe concrete is neglected.

4. The modulus of elasticity of concrete in compression as wellas that of the steel in tension is constant. The distribution ofcompressive stress is therefore rectilinear.

The notation and formulas used in analyzing the test results arebased upon the notation and formulas used in the 1924 report ofthe Joint Committee on Standard Specifications for Concrete andReinforced Concrete,11 with modifications made necessary by theaddition of the tiles. The units employed in the notation and cal-culations are inches and pounds.

In that report the subscript c refers to concrete and s to steel.

To these is added t for the tiles. Thus, Ec Es , and Et equal modulusof elasticity of concrete, steel, and tile, respectively.

In comparing the observations with the computations on differ-

ent assumptions, the subscript was used to represent results com-

puted directly from deformations observed during the test. Thus

fs0=Es es0 is the tensile stress in the longitudinal reinforcementcomputed from the observed elongation es0 .

In studying the effects of the tiles a distinction has to be madebetween the increased stiffness of the structure which is determined

by the relations between the deformations and loads and the in-

creased strength of the strucure which is determined by the momentswhich produced failure.

The subscript ( d ) is used to represent values modified empiricallyto take account of the presence of the tiles in the combination

beams in determining stiffness relations; that is, corresponding to

deformations and loads below the maximum.Similarly, the subscript (m ) is used to represent values modified

empirically to take account of the presence of the tiles in increas-

ing the strength of the structure; that is, for computations using

the loads which produced failure.

The symbols employed are collected for convenience of reference.Those marked with an asterisk are identical in meaning with the

11 Report of the Joint Commtitee on Standard Specifications for Concrete and Rein-forced Concrete (1924), Proc. Amer. Soc. for Testing Materials, 24, 1924.

486 Technologic Papers of the Bureau of Standards [Voi.19

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Tests of Hollow Tile and Concrete Slabs 487

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Tests of Hollow Tile and Concrete Slabs 489

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stoT*] Tests °f Hollow Tile and Concrete Slabs 491

symbols used in. the 1924 report of the Joint Committee for Con-

crete. The others have modified meanings as explained.It should be noted that all symbols and formulas refer to one

unit of width of a completed floor slab. In the combination beamsthis unit was a 16-inch concrete and tile rib, consisting of 4 inches

of concrete bordered by two half tiles. In the concrete beams

this unit was one-half the width of the beams. Thus, each beamtested represented two units of width of a floor slab. The weightsof the beams were disregarded in all calculations.

*AB = effective cross-sectional area of steel reinforcement in tension.*& = width of rectangular section of concrete or width of concrete

flange in T beam.Note.—The beams with topping (H—l, H-2, H-3, fig. 1) are con-

sidered as T beams.

& d = width of concrete plus an empirical correction proportionalto the thickness of the vertical tile shells and webs to takeaccount of the increased stiffness of the beams due tothe tiles.

b d = b + 2 (s + w) -j*

6m = width of concrete plus a similar empirical correction to takeaccount of the increased strength of the beam in bendingdue to the tiles.

Tf

6m = 6 + 1.3 (s+w) p-*

&teo = the equivalent increase in b due to the tiles, computed fromthe observed strain eco in the concrete. (See fig. 12.)

&tko = the equivalent increase in b due to the tiles, computed fromthe observed ratio fc of depth of neutral axis to depth d.

(See fig. 13.)

& tA = the equivalent increase in b due to the tiles, computed fromthe observed deflection of the beam A . (See fig. 14.)

b' = width of rectangular section of concrete or width of stemin T beam.

Note.—This modification of the standard notation makes the shearformula for rectangular and T beams identical in form.

b'm = width of concrete web plus an empirical correction propor-tional to the thickness of the vertical tile shells and webs.

b,

m = b' + 2(s + w)

*d = depth from compression surface of beam to center of longi-tudinal tension reinforcement.

eco = observed strain in the extreme fiber of concrete.

492 Technologic Papers of the Bureau of Standards [vol. 19

e so = observed strain in the steel measured on the bottom of thebars.

e to = observed strain in the extreme fiber of the tiles.*EC = modulus of elasticity of concrete in compression.Es = modulus of elasticity of steel in tension = 29,000,000 lbs. /in. 2 ,

instead of 30,000,000 as adopted in joint committee re-

port. (See Table 1.)

Et = modulus of elasticity of tile in compression.*/ = compressive stress in extreme fiber of concrete. Here com-

puted by the formula

Jc n\l-Tc)

conveniently expressed for rectangular beams as

2M/.

Jcjbd2

/od = compressive stress in extreme fiber of concrete in compositebeams computed by the above formula by replacing1c, j, and b, by Tc d , j d , and b d .

/cm = compressive stress in extreme fiber of concrete in com-posite beams computed by the above formula by replac-ing Tc, j, and b by Jcm , jm and bm .

*/s = tensile stress in longitudinal reinforcement. Here com-M

puted by the formulafs= a -j '

/6d = tensile stress in longitudinal reinforcement of compositebeams computed by the above formula by replacing

i by id./sm = tensile stress in longitudinal reinforcement of composite

beams computed by the above formula by replacing

j by jm-

/80 = tensile stress in longitudinal reinforcement computed fromthe measured deformation. /so = .E^so-

*j= ratio of lever arm of resisting couple to depth d, conveniently

Tc

expressed for rectangular beams as j = l — ^«

yd = ratio of lever arm of resisting couple to depth d in compositebeams, computed by the above formula by replacing fcby Tcd .

jm= ratio of lever arm of resisting couple to depth d in compositebeams, computed by the above formula by replacing Tcby Tcm .

staZm

]Tests °f Hollow Tile ancl Concrete Slabs 493

;= ratio of lever arm. of resisting couple to depth d in composite

beams, computed from observed deformations by theabove formula by replacing Tc by Jc .

*Jc = ratio of depth of neutral axis to depth d. Here computedby the formula

—

For rectangular beams

I" = -y/2pn + (pn) 2— pnFor T beams

^ =^(2nA + 2^)(aSSUmedn==15)

frd = ratio of depth of neutral axis to depth d computed by theabove formulas by replacing p and t by pd and td .

itm = ratio of depth of neutral axis to depth d computed by theabove formula by replacing p by pm .

Tc = ratio of depth of neutral axis to depth d calculated fromobserved deformations.

fc =t'co "r eG

*Z = span length of beam (distance from center to center ofsupports)

.

*M= bending moment.*n = ratio of modulus of elasticity of steel to that of concrete.

n^*p = T-|= ratio of effective area of tensile reinforcement to effective

area of concrete in beams. Corresponding to this also

:

2>d=A andpm= _4|

s = thickness of one vertical tile shell (outer wall). (SeeTable 3.)

*t = Thickness of the concrete flange of T beams.Note.—The composite beams with topping (H-l, H-2, H-S, fig. 1)are considered as T beams.

t d = thickness of the concrete flange plus thickness of top shellof tile in contact with concrete in composite beams withtopping.

v = shearing stress.

This differs from the notation of the joint committee inthat j is used instead of j.

494 Technologic Papers of the Bureau of Standards iroi. 19

vm = shearing stress computed by the above formula for thecomposite beams by replacing b' by b'm .

*y= total shear, pounds.w = thickness of one vertical tile web (partitions dividing the

tile into cells). (See Table 3.)

s = depth from compression surface of beam to resultant ofcompressive stresses.

A = observed deflection at the center of beam.A d = deflection of the center of the beam, computed by the

formula. 12

I2

Ad = g^(e 8 + ec )

where q is a constant depending on manner of loading.

2 = 0.105 for these tests, and

e B =fy with EB taken as 29,000,000 lbs./in. 2E s

ec =S^ with E taken as 3,625,000 lbs./in. 2 correspondingto 71 = 8.

By comparing the curves in Figures 8, 9, 10, and 11 and the ex-perimental data in Table 4 for the concrete beams with those for

the combination beams it is apparent that the tiles were effective in

reducing the compressive deformations in the concrete, the deflec-

tions, and the values of h . The hard tiles had a greater effect thanthe soft tiles. The average of the computed values of &d given inTable 4 are, for the concrete beams, slightly smaller than the average

determined by tests. This is in accord with the results of other

tests 13 and is to be expected on account of the inexactness of the

assumptions upon which the formula employed is based. The tensileresistance of the concrete which is neglected in the formula probably

had an important effect at low loads, and the deviation of the stress-strain relation for the concrete from the assumed linear relationprobably had an important effect at the higher loads. However,for the combination beams the averages of the computed values fork& are greater than the test values 7e ; that is, the effect of the tileswas, in all cases, to cause the neutral axis to lie above the position

it would have taken if the concrete were alone resisting the compres-sive stresses.

Although there are a number of methods which may be used incomparing the concrete beams with the combination beams without

12 G. A. Maney, "Relation between deformation and deflection in reinforced concrete beams " Proc.A

. S. T M., 14, Pt. II, p. 311; 1914.13 Humphrey and Losse, The Strength of Reinforced Concrete Beams—Results of Tests

of 333 Beams (first series). B. S. Tech. Paper No. 2.

stZZ"S

~\ Tests °f Hollow Tile and Concrete Slabs 495

topping to estimate the effect of the tiles upon the deformations of

the beams, it is of obvious advantage to employ as simple a method

as can be found. Probably the least difficult method to employ in

design is to consider that each concrete and tile rib is, as far as

deformations are concerned, equivalent to a homogeneous, rectangu-

lar concrete section to which the ordinary principles of analysis maybe applied. If, in the combination beams without topping, the size,shape, and design of the tiles are the same, and the distribution of

the compressive deformations is similar in tiles possessing different

properties, the effect of the tiles in increasing the breadth of the

equivalent rectangular concrete section should be proportional to theTBI

ratio _*; that is, the amount by which the breadth of a concrete

rib should be increased to form the equivalent concrete section, hav-

ing for the same deformations the same resisting moment as the com-

bination beam, would be equal to the ratio —1 multiplied by a factorE

whose value could be determined experimentally. The value of thisfactor would be constant only for tiles of exactly the same dimen-

sions. Since the outside dimensions and total weights of tiles of any

given design must be very nearly equal in order to fulfill the re-

quirements of a specification, it follows that the thickness of the

shells and webs of tiles, equal in weight, must vary inversely withthe bulk density of the material of which the tile is composed. Thevalue of the experimental factor, therefore, will vary in some man-ner, with variations in the thickness of the tile shells and webs. Thedimensions of the tiles in the combination beams without toppingwere approximately the same except for the thicknesses of the ver-tical shells and webs. The discussion so far has referred only to therelation between the deformations of the beams and bending mo-ments less than the maximum. A similar method would seem to bethe simplest way of comparing the strengths of the combinationbeams without topping with those of the concrete beams. The em-pirical factor, however, should not be expected to be the same in

both cases. As will be shown later, the results indicate that at loadsless than the maximum each concrete and tile rib was approximatelyequivalent, in resisting deformations, to a rectangular concrete beam

having a width at least equal to 2 (s-\-w) -w+S- Similarly, on the

basis of the maximum bending moments actually resisted by thecombination beams, each concrete and tile rib was approximatelyequivalent in strength to a rectangular concrete beam having a width

rp

at least equal to 1.3 (s-{-w) ^-{-b, the empirical factor in this case

496 Technologic Papers of the Bureau of Standards itoi.jd

being smaller than in the case of the deformations. Both coefficientsgiven are empirical, and although no direct expression appears forthe effect of the top shells of the tiles it is obvious that the effect of

their resistance is included. It is also obvious that for tiles with a

different distribution of thickness between vertical and horizontalshells and webs different values for these empirical coefficients shouldbe expected.

Since the beams with a 2-inch concrete topping were similar toconcrete T beams, it is more convenient to consider them as suchin making comparisons than to use the method employed in compar-ing the combination beams without topping. On account of theposition of the tiles relative to the neutral axis the assistance of the

tiles in resisting compressive stresses in the beams with topping

was not as great as in those without the topping. The greater areaof the tiles in contact with the concrete should, however, have

caused a more uniform distribution of the stress throughout thetiles. Since only one grade of tiles was used in the beams withtopping, no conclusions co'uld be drawn as to the effect of differingphysical properties of the tiles upon beams of this type, although it

seems certain that such an effect must exist. The simplest methodto employ seemed to be to consider that the effect of the tiles wasapproximately equivalent to adding to the thickness of the concrete

flange an amount proportional to the thickness of the top shell ofthe tile in contact with it, multiplied by an empirically determined

factor. As will be shown in the discussion later, the effect upondeformation and strength in these beams was practically the same,

so that the same factor could be used in both cases. The resultsindicated that for all practical purposes this factor could be taken

as one. This would probably be modified if the modulus of elas-

ticity of the tiles differed greatly from the modulus of elasticity of

the concrete.

(b) CONCRETE BEAMS

The results of tests of the concrete beams are in accord with thosefound in previous investigations in that (1) the observed values of

k were greater than the computed values h; 14 (2) the strain in the

extreme fiber at maximum loads was greater than the maximumstrain in the corresponding test cylinders; 14 ' 15 (3) the compressive

stresses in the beams for the maximum loads when computed by thestraight line formula greatly exceeded the stresses which caused thefailure of the test cylinders and prisms. 16

.In beams of ordinary

size and design the computed stresses in the reinforcement are

14 Humphrey and Losse, The Strength of Reinforced Concrete Beams—Results of Testsof 333 Beams (first series). B. S. Tech. Paper No. 2.

15 Bui. No. 175, Univ. of Wis., 1907.16 Slater and Zipprodt, " Compressive strength of concrete in flexure," Proc. Amer.

Concrete Inst., 16, 1920.

stan0113

]Tests of Hollow Tile and Concrete Slabs 497

greater than the stresses determined from observed deformations.17

It will be noted in Table 4 that for loads numbers 2 and 3 the ob-

served tensile stresses in beams B are greater than the computedstresses. The chief causes for this discrepancy are (1) use of the

straight line formula with very high stresses in the concrete; (2)the nominal area of the bars was 3 per cent greater than the meas-

ured area, and as the computed stresses were based upon the nomi-

nal area they should be increased by about 3 per cent; and (3) the

deformations measured on the bottom of the bars were considered

to be the average deformation of the steel, whereas the depth d used

in the computations was the distance from the compression surface

to the center of the bars. In the beams of ordinary depths the

deformations on the bottom of the reinforcement are nearly equal to

the average deformations of the bar, but in beams B the distancefrom the gauge lines to the centroid of the steel area was more than20 per cent of the average distance from the neutral axis to the cen-troid of the steel area, so that the stresses in the bottom of the re-

inforcement were greater than at the center, the difference probably

approaching 20 per cent at loads below the yield point in the steel.

If the measured deformations had been corrected linearly to thecenter of the reinforcement bars the computed stresses would haveexceeded the observed values slightly, and the results would then bein accord with the results of previous tests.

(c) combination beams with no topping

1. Concrete Deformations, Depth to the Neutral Axis, Deflec-tions, and Steel Stresses.—Since the width of the concrete and thedepth to the steel were not the same in all beams, some method ofreducing the test values of k ec0 , and A to a common basis must beemployed in order to compare the properties of the combinationbeams with the properties of the concrete beams and to determinethe effect of the properties of the tiles upon their action in the beams.Each combination beam may be considered to be equivalent to aconcrete beam of the same depth and containing the same amountof reinforcement and having a width such that its computed de-formation in the concrete, position of neutral axis, and deflectionwould be equal to the observed values. It is not to be expected thatconcrete beams equal in width to the values given by such computa-tions will actually be equivalent to the corresponding beams, for, onaccount of the variations between the conditions in the beams andthe assumed conditions upon which the formulas are based, it isimpossible for the computed values to equal the test values for all

17 Westergard and Slater, " Moments and stresses in slabs," Proc. Arner. Concrete Inst.,17, 1921.

498 Technologic Papers of the Bureau of Standards [Voi.19

loads. However, by comparing the concrete beams with the com-

bination beams, some relation between the properties of the tile and

their effect upon the action of the beams under load, at loads less

than the maximum, may be seen.The effect of the tiles upon the compressive deformations m the

concrete.—In comparing the beams to determine the effect of thetiles upon the deformation in the concrete the width of rectangular

beams, for which the computed deformation in the concrete would

equal the measured deformation, were determined for three series

of loads, as shown in Figure 12. The difference, b te o, between thewidths of these equivalent concrete beams thus determined and the

net width o of the concrete ribs was considered to be a measure of theeffect of the tiles upon the deformations in the concrete. The valuesplotted in Figure 12 indicate that the effect of the tiles upon thecompressive deformations in the concrete was approximately equiva-

lent to adding widths of concrete to the ribs proportional to values

of (s-\-w) pr*- This relation is seen to hold for a wide range of loads.

The effect of the tiles upon the position of the neutral axis.—Fromthe average of the observed values of k given in Table 4 for similar

beams the values of p corresponding to k with the assumed valuen=15 were first computed. From the known area of reinforcementand known depth the width of beams corresponding to these valuesof p were then computed. The difference, & tko, between the width ofthe equivalent concrete beams, for which the computed depth to theneutral axis was equal to the observed depth and the net width bof the concrete ribs, was taken as a measure of the effect of the tiles

upon the depth of the neutral axis. The relation between the valuesplotted in Figure 13 indicates that the effect of the tiles upon theposition of the neutral axis was approximately equivalent to adding

Etwidths of concrete to the ribs proportional values of (s-\-w) -~r the

same quantity as above.The effect of the tiles upon the beam deflections.—In order to com-

pare the different beams to determine the effect of the tiles upon thedeflections, it was assumed that the effect of the differences in di-mensions were approximately given by Maney's formula modifiedas shown in the title of Figure 14. The relation between the valuesplotted in Figure 14 indicates that the effect of the tiles upon thebeam deflections was approximately equivalent to adding widths of

pi

concrete to the ribs again proportional to the values of (s-\-w) -^r-

It is obvious that values such as those given in Figures 12, 13, and14, which are functions of deformations and which indicate the effectof the tiles upon the deformations of the beams at loads less thanthe maximum, do not indicate the maximum strength of the con-

Parsons!Stang J

Tests of Hollow Tile and Concrete Slabs 499

struction or the value of the tiles in increasing the strength of the

beams. Beams of such a composite character may fail in some othermanner before the ultimate compressive strength of the constructionhas been developed. The failure may be caused by the failure of anindividual tile or by the failure of the bond between the tiles and con-crete or by the concentration of stress in a part of the concrete causedby the lack of continuity of the tiles. Furthermore, the average

UjU

4-

500 Technologic Papers of the BwreaM of Standards [Vol. X9

the increase in stiffness of the beams due to the tiles was approxi-mately equivalent to adding to each concrete rib a width of con-

crete greater than 2(s+w) -^r>

The computed tensile stresses in the reinforcement /sd and theobserved stresses /so are given in Table 4. For the combination

beams the computed stresses in the reinforcement were, in general,

greater than the observed stresses at the loads given.

b+ko

a W IZ 14 16

— b, inches

Id

>tko p dFig. 13.

—

Showing that the effect of the tile upon the position of the neutralaxis was approximately proportional to the product of modulus of elasticity

of the tiles by the thickness of the vertical shells and weos

In the formula 6tko=—f—

6

pa

p was taken as value given by the formula

P/Co

2

in whichlbs./in. 2

2m (1-fco)

15 and ko was the average value given in Table 4 for values of fso=16,000

2. Maximum Bending Moments and Computed Stresses.—Thecause of the failures of the combination beams containing hard tiles

was the tension failure of the reinforcement. In these beams there

was no spalling of the concrete and tiles before the primary failure

occurred, and it was evident that the full compressive strength of

the concrete and tiles had not been reached. Beams B, which had thesame cross sectional area as the sectional area of the two concrete

ribs in the combination beams, and five of the six combination beams

containing soft tiles failed in compression.

Parsons 1Stang< J

Tests of Hollow Tile and Concrete Slabs 501

Table 5 gives the maximum bending moments, causes of failures,and computed tensile and compressive stresses corresponding to the

maximum bending moments. It is seen that the maximum com-puted tensile stresses for the beams which failed in tension are

in fair agreement with the yield-point stress of 39,180 lbs./in. 2 found

in the tests of the coupon specimens.

It was noted in Figures 12, 13, and 14 that the effects of the tiles

upon the deformation in the concrete, the depth of the neutral axis,

and the deflection of the beams were each equivalent to the effect of

1o

UJ

502 Technologic Papers of the Bureau of Standards [vol. 19

Table 5.

—

Maximum bending moments, computed stresses, and causes of failuresfor long beams

Maxi-mum

bendingmoments2M

Computed stresses

Stressesin tilesfrommaxi-mum

deforma-tions

fto=etoEt

Beam numberTensilestresses,

steel

Aejmd

Compressivestresses

Cause of failure

Concrete

TmWmbmd2

Tile/tm

7cmEc

A-l _Lb.in.565, 200492, 000

Lbs./in. 2

40, 30035, 300

Lbs./in.'2,1501,890

Lbs./in.' Lbs./in.*

A-2 Do

Average _ 528, 600 37,800 2,020

B-l _ 358, 500327, 000237,000

28, 90026,50018,100

3,8403, 5302,360

Compression.Do.B-2 __

B-3 _ Do.

Average 307, 500 24,500 3,240

C-l 465, 000360, 000315, 600

36,00023, 400

3,8203,090

3,1002,500

1,9801,230

Diagonal tension.Compression.

Do.C-2C-3 1— __

Average J 412, 500

594, 000.505, 200513, 600

32, 200 3,460 2,800 1,610

D-l 41,90036, 700

37, 600

3,4303,1703,210

6,2505,7705,860

4,5003,0804,410

D-2 Do.D-3 Do.

Average 537, 600 38, 730 3,270 5,960 4.000

E-l 528,000454, 800534, 000

41, 20040, 10042, 200

3,1903, 3803,280

7,9608,4508,200

4,6605,1805,020

Do.E-2 Do.E-3 Do.

Average 503, 600 41, 170 3,280 8,200 4, 950

F-l... 477, 000477, 600420, 000

35, 60037, 00032, 400

3, 6504,0003,520

2,9603,2402,850

1,9201,7202,520

Compression.Do.F-2

F-3 Do.

Average 458, 200 35,000 3,720 3,020 2,050

G-l 540,000537,000570,000

40, 50042,00039,100

3, 5003,7803,210

6,3706,8905,850

3,4304,8003,430

G-2 DoG-3-__ _. Do.

Average 549, 000 40, 500 3,500 6,370 3,890

H-l 550, 500565, 500531,000

38, 80039,50039,500

2,0502,0902,190

Do.H-2_ Do.H-3_ Do.

Average 549,000 39, 270 2,110

1 One tile near the center of beam C-3 was broken before the test. The average given is of beams C-land C-2 only.

considered, but which, for any case, would be greater than two. Themaximum loads supported by the beams and the corresponding com-puted compressive stresses given in Table 5 indicate, however, that

the effect of the tiles upon the ultimate strength of the beams wasless than might be expected from their effect on the deformationsof the beams at low loads. A comparison of the load-deformationcurves of Figures 8, 9, 10, and 11 indicates that, although the strainsin the concrete of the combination beams were less than those in theconcrete beams B at a given load, the maximum strains developedin the combination beams before compression failures were con-

IS18 ] Tests °f HoUow Tile and Concrete Slabs 503siderably less than those in the concrete beams. The average maxi-mum compressive strain at the extreme fiber in beams F was about0.0020 inch per inch and in beams B about 0.0027 inch per inch. Thisdifference shows that the presence of the tiles did not increase the

strength of the beams as much as it did their stiffness. This is prob-ably due to the greater concentration of compressive stresses in the

concrete around the joints in the composite beams. Consequently, an

empirical correction in strength formulas must be less than that used

in deflection or strain formulas.

The maximum compressive strength of the concrete and tiles inthe combination beams containing hard tiles was not developed,

but it may be conservatively measured by the maximum stress

resisted. If in the general formula fc = , ., -, 2 M is taken as theaverage of the maximum bending moments for similar beams and

/c is taken as 3,240 lbs./in.2 (the average of the maximum com-

puted stresses in the concrete beams which failed in compression)

and the equation is solved for & by a series of approximations in

which k and j are given values corresponding to the new values of &,it is found that these widths will in all cases be equal to or greater

Etthan 1.3 (s + w) ~^r-\-h. The maximum computed stresses in the

Wconcrete

/

cm computed on the basis that &m = 1.3 (s + w) w +Jare given in Table 5, and it is seen that the average of the maximumcomputed stresses in the concrete of the combination beams wasgreater than the average of the maximum computed stresses in theconcrete of beams B. On the assumption, therefore, that the con-crete in the combination beams without topping was capable ofresisting a compressive stress equal to the average maximum stressin the concrete beams which failed in compression, each concreteand tile rib of the combination beams (equivalent to one-half thebeam as a whole) under the action of bending moments was equiva-lent in strength to similar concrete beams having a width equalto the width of one concrete rib plus the empirical correction for

the tile 1.3 (s+w) ^ with Ec taken as 2,000,000 lbs./in. 2The maximum observed and computed stresses in the tiles are

given in Table 5. The maximum observed stress ft0 is the productof the maximum deformation in one gauge line on each beam by theaverage modulus of elasticity found by the tests of the corre-sponding individual tiles. The computed stresses /tm given are theproducts of /cm corresponding to the maximum loads and the ratioEt-j? in which Ec is taken as 2,000,000 lbs./in. 2 The stresses com-

504 Technologic Papers of the Bureau of Standards ivoi. 19

puted from the observed deformations are less than maximumstresses in the tiles, for the measured deformations give the average

deformations over the 8-inch gauge length, and, as the stresses in

the tiles were caused by the bond between them and the concrete,the maximum intensity of the stresses was at the surface of the tilesin contact with the concrete. It would be expected on account ofthe shape of the stress-deformation curve for concrete in compres-

sion, that as the stresses in the concrete became high enough tocause a marked increase in the amount of deformations producedby a given increase in stresses the tiles would, on account of theirstraight-line stress-deformation relation, be stressed proportionately

more. It is seen, however, that the observed stresses in the tiles

were, even for the greatest loads, less than those computed under

the assumption that ftm =/cm -^r •

In no case did the maximum observed stresses /t0 in the tiles equalor exceed the compressive strength of the tiles determined by thetests of 10 single tiles of each lot, but in several cases the maximumcomputed stresses ftm exceeded their average compressive strength.It was not expected that such computations would yield exact valuesof stresses, but the tests indicate that the computed stresses in thetiles may equal or exceed the compressive strength of the tiles beforea compression failure occurs.

3. Effect of Mortar Joints.—Beams C may be compared withbeams F and beams D with beams G to determine the effect of themortar in the cross joints. The mortar in beams F and Gr did notaffect the stiffness of the beams at low loads and seemed to have but

slight effect at loads near the maximum. The computed stresses inthe extreme fiber of the concrete (see Table 5) for the maximumbending moments were about 6.5 per cent greater in the beams with

mortar joints than in those with open joints. The tests were notsufficient to show the effect of the mortar on the shearing strength

of the beams. Although these tests were not conclusive, the effect

of the mortar joints on the stiffness and strength of these beams

evidently was not great.

(d) combination beams with topping

The test results given in Table 4 indicate that the deformations ofbeams H (see fig. 1) were more closely estimated by computationswhich considered the beams to consist of concrete T beams whichhad flange thicknesses equal to the sum of the thickness of the con-

crete flange and the thickness of the top shell of the tiles, than by

considering the tiles to be only inert fillers. A comparison of thevalues h based upon the net section of the concrete with the experi-

mental values k indicates that such computations which do not

Parsons] Tests of Hollow Tile and Concrete Slabs 505

consider the effect of the tiles result in values much too high. Thevalues &a, computed on the assumption that the flanges consisted of

the concrete and 1 X the thickness of the top shells of the tiles, aremore closely in agreement with the test results. The compressivestresses computed on the same assumption were, for the three loads

given in Table 4, 50, 48, and 42 per cent' greater than stresses

computed from deformations with Ec taken as 2,000,000 lbs./in.2Although Ec was probably greater than this value, it is seen that ifhigher values of Ec up to 2,800,000 lbs./in.2 were taken the stresseswere conservatively estimated. The average observed stresses in thereinforcement were less than the average computed stresses. Exceptfor loads near the maximum, the computed deflections were greaterthan those observed. These results seem to indicate that the topshells of the tiles were somewhat similar in effect to an equal thick-ness of concrete in their effects upon the deformations of the beams.The maximum loads supported by beams H were probably con-

siderably less than the loads which would have been required to

develop the maximum compressive strength of the concrete andtiles. The yield point in the reinforcement in each of these beamswas reached before there were any visible signs of compression fail-

ures. The load-deformation curves of Figure 11 show that theaverage of the maximum deformations developed in the concrete wasabout 0.0007 inch per inch, which is less than one-third the strain

which usually accompanies the compression failures of concrete

beams. In the beams which failed by compression the averagestrain at the extreme fiber in the concrete beams B at failure was0.0027 inch per inch and in the composite beams F 0.0020 inch perinch. Although the increases in the loads are not to be expected to

be in proportion to the increases in deformations beyond this point,

it is probable that a considerable increase in loads would have beennecessary before compression failures would have been produced if

the yield point in the steel had been sufficiently high. It was notedthat the maximum compressive strains in the composite beams with-out topping were less than those in the concrete beams. The dis-continuity of structure in the extreme fiber producing concentrated

stresses in the concrete, which was present in the composite beamswithout topping, was not present in those with topping. Conse-quently, it would not be expected that the tiles in the beams withouttopping would have an important effect upon the maximum com-pressive strains.

The area of the tiles in contact with the concrete was much greaterin the beams with topping than in those without. The deformationin the tiles should, therefore, be more nearly equal to that whichwould occur in concrete at the same relative position with respect tothe neutral axis than in beams without a topping.

506 Technologic Papers of the Bureau of Standards [Vol. 19

On account of the distance of the tiles from the extreme fiberthey would bear relatively less stress than in the beams without

topping. Since failure of the tiles is not to be expected, the in-

crease of stiffness due to the tiles should give a corresponding

increase in strength. Therefore, concrete beams equivalent in stiff-

ness to the combination beams with topping should also be ex-

pected to be equivalent in strength. This was not found to be

true for the combination beams without topping.

(e) DISTRIBUTION OF COMPRESSIVE DEFORMATIONS ACROSS THE BEAMS

Figures 15 and 16 show the deformations for each gauge line

in the concrete and tiles for the two loads which produced stresses

of approximately 16,000 and 32,000 lbs./in. 2 in the reinforcement.

In general, the deformation in a concrete rib was greater than in the

adjacent tile, and the deformation in the tiles was greatest near the

concrete. The deformations measured in the outer tiles of the beamscan not be considered to represent those which would be expected to

occur in a complete slab, so in considering the relation of the defor-

mation in the tiles to that in the concrete the values obtained for the

center row of tiles were used. There was a wide variation in theratio of the deformation in the tiles to that in the concrete. Theaverage ratios for the center row of tiles are as follows : Beams E,side shells 0.96, center webs 0.86; beams D and G, side shells 0.91,center webs 0.77 ; beams C and F, side shells 0.80, center webs 0.66.

It is not believed that the ratios of deformations are useful for

determining the quantitative effect of the tiles in resisting stresses,

for the deformations measured in the tiles do not necessarily repre-

sent either the maximum or the average deformations. The gaugelines were in the center of the shells and webs and covered but 8inches of the center of the tile, and as the deformation of the tileswas produced chiefly through the bond between them and the con-crete the maximum deformation in a tile should occur at the surfacein contact with the concrete. Furthermore, the distribution of stress

along the 8-inch gauge line was probably not uniform, and it is cer-tain that a small length near the ends of the tiles was stressed butlittle if at all. The uncertainty of the distribution of the stressthroughout the tiles and concrete either as to direction or intensitymakes it impracticable to attempt to use the values of deformationobtained to compute the value of the tiles in assisting the concrete.

3. SHEAR TESTS

(a) BEAMS WITHOUT WEB REINFORCEMENT

Table 6 gives the maximum loads, maximum computed shearingstresses, spans of the supports, distance between the loads, and thecauses of failures. The formulas employed in making the compu-

Parsom "I8tan& J

Tests of Hollow Tile and Concrete Slabs 507

O

o3•8

3

3

Deformation — in./in.

5 ft ftfc b fc>

:^ii

;;& v> ;:

fill

m -^-g-.-i!;

S&

c>Q i\

031

1 I

xvl

508 Technologic Papers of the Btcrecw of Standards ivui. &

11111

j >»////»/,I

y/w/M

jW/M

1^R^r—

—

11

5:

1 1» ti5 -4=§ $*1 1*«>

4

Parsons "IStatic J

Tests of Hollow Tile and Concrete Slabs 509

tations are given in the notation. The values j determined fromdeformations corresponding to loads which produced a stress of

16,000 lbs./in. 2 in the reinforcement were used in all computations.

Table 6.

—

Results of shear tests

A. BEAMS WITHOUT WEB REINFORCEMENT[Span of supports equals 14 feet]

Date made

Storage

Agea